Problem: One day mum asked Petya to sort his toys and get rid of some of them. Petya found a whole box of toy spiders. They were quite dear to him and the boy didn't want to throw them away. Petya conjured a cunning plan: he will glue all the spiders together and attach them to the ceiling. Besides, Petya knows that the lower the spiders will hang, the more mum is going to like it and then she won't throw his favourite toys away. Help Petya carry out the plan.

A spider consists of k beads tied together by k - 1 threads. Each thread connects two different beads, at that any pair of beads that make up a spider is either directly connected by a thread, or is connected via some chain of threads and beads.

Petya may glue spiders together directly gluing their beads. The length of each thread equals 1. The sizes of the beads can be neglected. That's why we can consider that gluing spiders happens by identifying some of the beads (see the picture). Besides, the construction resulting from the gluing process should also represent a spider, that is, it should have the given features. 

After Petya glues all spiders together, he measures the length of the resulting toy. The distance between a pair of beads is identified as the total length of the threads that connect these two beads. The length of the resulting construction is the largest distance between all pairs of beads. Petya wants to make the spider whose length is as much as possible.

<image> <image>

The picture two shows two spiders from the second sample. We can glue to the bead number 2 of the first spider the bead number 1 of the second spider. The threads in the spiders that form the sequence of threads of maximum lengths are highlighted on the picture.

Input

The first input file line contains one integer n (1 ≤ n ≤ 100) — the number of spiders. Next n lines contain the descriptions of each spider: integer ni (2 ≤ ni ≤ 100) — the number of beads, then ni - 1 pairs of numbers denoting the numbers of the beads connected by threads. The beads that make up each spider are numbered from 1 to ni.

Output

Print a single number — the length of the required construction.

Examples

Input

1
3 1 2 2 3


Output

2


Input

2
3 1 2 1 3
4 1 2 2 3 2 4


Output

4


Input

2
5 1 2 2 3 3 4 3 5
7 3 4 1 2 2 4 4 6 2 7 6 5


Output

7

Solution (in JAVA):

Solution:
import java.awt.Point;
import java.io.*;
import java.math.BigInteger;
import java.util.*;
import java.util.Map.Entry;

import static java.lang.Math.*;

public class F {
       
        final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE")!=null;
        BufferedReader in;
        PrintWriter out;
        StringTokenizer tok = new StringTokenizer("");
       
        void init() throws FileNotFoundException{
                        in = new BufferedReader(new FileReader("input.txt"));
                        out = new PrintWriter("output.txt");
        }
       
        String readString() throws IOException{
                while(!tok.hasMoreTokens()){
                        tok = new StringTokenizer(in.readLine());
                }
                return tok.nextToken();
        }
       
        int readInt() throws IOException{
                return Integer.parseInt(readString());
        }
       
        long readLong() throws IOException{
                return Long.parseLong(readString());
        }
       
        double readDouble() throws IOException{
                return Double.parseDouble(readString());
        }
       
        public static void main(String[] args){
                new F().run();
        }
       
        public void run(){
                try{
                        long t1 = System.currentTimeMillis();
                        init();
                        solve();
                        out.close();
                        long t2 = System.currentTimeMillis();
                        System.err.println("Time = "+(t2-t1));
                }catch (Exception e){
                        e.printStackTrace(System.err);
                        System.exit(-1);
                }
        }
       
        int n, m;
        ArrayList<Integer>[] graph;
        int[] d;
        boolean[] used;
        
        void solve() throws IOException{
            n = readInt();
            long res = 0;
            for (;n-- > 0;){
                m = readInt();
                if (m == 1) continue;
                graph = new ArrayList[m];
                for (int k = 0; k < m; k++){
                    graph[k] = new ArrayList<Integer>();
                }
                for (int j =0 ; j < m - 1; j++){
                    int from = readInt() - 1;
                    int to = readInt() - 1;
                    graph[from].add(to);
                    graph[to].add(from);
                }
                bfs(0);
                int I = -1, max = 0;
                for (int i = 0; i < m; i++){
                    if (d[i] > max){
                        max = d[i];
                        I = i;
                    }
                }
                bfs(I);
                max = 0;
                for (int i = 0; i < m; i++){
                    max = max(max, d[i]);
                }
                res += max;
            }
            out.print(res);
        }     
        
        void bfs(int begin){
            d = new int[m];
            used = new boolean[m];
            used[begin] = true;
            d[begin] = 0;
            ArrayDeque<Integer> q = new ArrayDeque<Integer>();
            q.add(begin);
            while (q.size() > 0){
                int from = q.poll();
                for (int to: graph[from]){
                    if (!used[to]){
                        d[to] = d[from] + 1;
                        used[to] = true;
                        q.add(to);
                    }
                }
            }
        }
       
        static class MyAlgo{
               
                long gcd(long a, long b){
                        if (a == 0)     return b;
                        return gcd(b % a, a);
                }
               
                long lcm(long a, long b){
                        return a / gcd(a, b)*b;
                }

                long[] gcdPlus(long a, long b){
                        long[] d = new long[3];
                        if (a == 0){
                                d[0] = b;
                                d[1] = 0;
                                d[2] = 1;
                        }else{
                                d = gcdPlus(b % a, a);
                                long r = d[1];
                                d[1] = d[2] - b/a*d[1];
                                d[2] = r;
                        }
                        return d;
                }
               
                long binpow(long a, int n){
                        if (n == 0)     return 1;
                        if ((n & 1) == 0){
                                long b = binpow(a, n/2);
                                return b*b;
                        }else return binpow(a, n - 1)*a;
                }
               
                long binpowmod(long a, int n, int m){
                        if (m == 1) return 0;
                        if (n == 0)     return 1;
                        if ((n & 1) == 0){
                                long b = binpowmod(a, n/2, m);
                                return (b*b) % m;
                        }else return binpowmod(a, n - 1, m)*a % m;
                }
               
                long f(long n, int x, int k){ //Кол-во десятичных чисел (включая 0), содержащих в себе цифры от 0 до k-1
                        if (n == 0)     return 1;
                        long b = binpow(10, x - 1);
                        long c = n / b;
                        return (c < k? c: k)*binpow(k, x - 1) + (c < k? 1: 0)*f(n % b, x - 1, k);
                }
               
                long fib(int n){
                        if (n == 0) return 0;
                        if ((n & 1) == 0){
                                long f1 = fib(n/2 - 1);
                                long f2 = fib(n/2 + 1);
                                return f2*f2 - f1*f1;
                        }else{
                                long f1 = fib(n/2);
                                long f2 = fib(n/2 + 1);
                                return f1*f1 + f2*f2;
                        }
                }
               
                BigInteger BigFib(int n){
                        if (n == 0) return BigInteger.ZERO;
                        if ((n & 1) == 0){
                                BigInteger f1 = BigFib(n/2 - 1);
                                f1 = f1.multiply(f1);
                                BigInteger f2 = BigFib(n/2 + 1);
                                f2 = f2.multiply(f2);
                                return f2.subtract(f1);
                        }else{
                                BigInteger f1 = BigFib(n/2);
                                f1 = f1.multiply(f1);
                                BigInteger f2 = BigFib(n/2 + 1);
                                f2 = f2.multiply(f2);
                                return f2.add(f1);
                        }
                }
               
                double d(Point p1, Point p2){
                        return sqrt(d2(p1, p2));
                }
               
                double d2(Point p1, Point p2){
                        return (p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y);
                }
               
                boolean IsProbablyPrime(long n){
                        if (n == 1)     return false;
                        if ((n & 1) == 0) return false;
                        for (int j = 3; j < sqrt(n) + 1; j += 2){
                                if (n % j == 0) return false;
                        }
                        return true;
                }

                int[] Sieve(int n){
                        boolean[] b = new boolean[n+1];
                        Arrays.fill(b, true);
                        b[0] = false;
                        b[1] = false;
                        long nLong = n;
                        int j=0;
                        for (int i = 1; i <= n; i++) {
                                if (b[i]){
                                        j++;
                                        if (((long)i)*i <= nLong) {
                                                for (int k = i*i; k <= n; k += i) {
                                                        b[k] = false;
                                                }
                                        }
                                }
                        }
                        int[] p = new int[j];
                        Arrays.fill(p, 0);
                        j=0;
                        for (int i = 2; i <= n; i++) {
                                if (b[i]){
                                        p[j]=i;
                                        j++;
                                }
                        }
                        return p;
                }
               
                int[][] Palindromes(String s){
                        char[] c = s.toCharArray();
                        int n = c.length;
                        int[][] d = new int[2][n];
                        int l = 0, r = -1;
                        for (int i = 0; i < n; i++){
                                int j = (i > r? 0: min(d[0][l+r-i+1], r-i+1)) + 1;
                                for (; i - j >= 0 && i + j - 1< n && c[i-j] == c[i+j-1]; j++);
                                d[0][i] = --j;
                                if (i + d[0][i] - 1 > r){
                                        r = i + d[0][i] - 1;
                                        l = i - d[0][i];
                                }
                        }
                        l = 0;
                        r = -1;
                        for (int i = 0; i < n; i++){
                                int j = (i > r? 0: min(d[1][l+r-i], r-i)) + 1;
                                for (; i - j >= 0 && i + j < n && c[i-j] == c[i+j]; j++);
                                d[1][i] = --j;
                                if (i + d[1][i] > r){
                                        r = i + d[1][i];
                                        l = i - d[1][i];
                                }
                        }
                        return d;
                }
               
                public static class SuffixAvtomaton{
                       
                        class State{
                               
                                int length;
                                State link;
                                HashMap<Character, State> next;
                                boolean terminal;
                               
                                public State(){
                                        length = 0;
                                        link = null;
                                        next = new HashMap<Character, State>();
                                        terminal = false;                               }
                        }
                       
                        ArrayList<State> st;
                        State last;
                       
                        public SuffixAvtomaton(String s){
                                Init();
                                for (int i = 0; i < s.length(); i++){
                                        add(s.charAt(i));
                                }
                                Marking();
                        }
                       
                        void Init(){
                                last = new State();
                                st = new ArrayList<State>();
                                st.add(last);
                        }
                       
                        void add(char c){
                                State newLast = new State();
                                st.add(newLast);
                                newLast.length = last.length + 1;
                                State p;
                                for (p = last; p != null &&!p.next.containsKey(c); p = p.link){
                                        p.next.put(c, newLast);
                                }
                                if (p == null){
                                        newLast.link = st.get(0);
                                }else{
                                        State q = p.next.get(c);
                                        if (q.length == p.length + 1){
                                                newLast.link = q;
                                        }else{
                                                State clone = new State();
                                                clone.link = q.link;
                                                clone.length = p.length + 1;
                                                clone.next.putAll(q.next);
                                                for (; p!= null; p = p.link){
                                                        if (p.next.get(c) == q) p.next.put(c, clone);
                                                }
                                                q.link = newLast.link = clone;
                                        }
                                }
                                last = newLast;
                        }
                       
                        void Marking(){
                                for (State term = last; term != null; term = term.link){
                                        term.terminal = true;
                                }
                        }
                       
                        int SubStrings(){
                                HashMap<State, Integer> d = new HashMap<State, Integer>();
                                d.put(st.get(0), 0);
                                ArrayList<State> list = new ArrayList<State>();
                                list.add(st.get(0));
                                while (list.size() != 0){
                                        State p = list.get(0);
                                        list.remove(0);
                                        for (State s: st){
                                                if (s.next.containsValue(p)){
                                                        if (d.containsKey(p)){
                                                                int x = d.get(p) + 1;
                                                                d.put(s, x);
                                                                list.add(s);
                                                        }
                                                }
                                        }
                                }
                                return d.get(last);
                        }
                }
               
                public class Permutation {
                       
                        int[] a;
                        int n;
                       
                        public Permutation(int n){
                                this.n=n;
                                a=new int[n];
                                for (int i=0; i<n; i++){
                                        a[i]=i;
                                }
                        }
                       
                        public boolean nextPermutation(){ //Пишется с do{}while(nextPermutation(a));
                                int i=n-1;
                                for (i=n-2; i>=0; i--){
                                        if (a[i]<a[i+1]){
                                                break;
                                        }
                                }
                                if (i==-1){
                                        return false;
                                }
                                int jMin=i+1;
                                for (int j=n-1; j>i; j--){
                                        if (a[i]<a[j]&&a[j]<a[jMin]){
                                                jMin=j;
                                        }
                                }
                                swap(i, jMin);
                                for (int j=1; j<=(n-i)/2; j++){
                                        swap(i+j, n-j);
                                }
                                return true;
                        }
                       
                       
                        public int get(int i){
                                return a[i];
                        }
                       
                        void swap(int i, int j){
                                int r=a[i];
                                a[i]=a[j];
                                a[j]=r;
                        }
                }
               
                public class Fraction implements Comparable<Fraction>, Cloneable{
                       
                        public final Fraction FRACTION_ZERO = new Fraction();
                        public final Fraction FRACTION_ONE = new Fraction(1);
                        public long numerator = 0;
                        public long denominator = 1;
                       
                        public Fraction(){
                                numerator = 0;
                                denominator = 1;
                        }
                       
                        public Fraction(long numerator){
                                this.numerator = numerator;
                                denominator = 1;
                        }
                       
                        public Fraction(long numerator, long denominator){
                                this.numerator = numerator;
                                this.denominator = denominator;
                                Cancellation();
                        }
                       
                        public Fraction(double numerator, double denominator, int accuracy){
                                this.numerator = (long)(numerator*pow(10,accuracy));
                                this.denominator = (long)(denominator*pow(10,accuracy));
                                Cancellation();
                        }
                       
                        public Fraction(String s){
                                if (s.charAt(0) == '-'){
                                        denominator = -1;
                                        s = s.substring(1);
                                }
                                if (s.indexOf("/") != -1){
                                        denominator *= Integer.parseInt(s.substring(s.indexOf("/") + 1));
                                }
                                if (s.indexOf(" ") != -1){
                                        numerator = Integer.parseInt(s.substring(0, s.indexOf(" "))) * abs(denominator) + Integer.parseInt(s.substring(s.indexOf(" ") + 1, s.indexOf("/")));
                                }else{
                                        if (s.indexOf("/") != -1){
                                                numerator = Integer.parseInt(s.substring(0, s.indexOf("/")));
                                        }else{
                                                numerator = Integer.parseInt(s)*abs(denominator);
                                        }
                                }
                                this.Cancellation();
                        }
                       
                        void Cancellation(){
                                long g = gcd(abs(numerator), abs(denominator));
                                numerator /= g;
                                denominator /= g;
                                if (denominator < 0){
                                        numerator *= -1;
                                        denominator *= -1;
                                }
                        }
                       
                        public String toString(){
                                String s = "";
                                if (numerator == 0){
                                        return "0";
                                }
                                if (numerator < 0){
                                        s += "-";
                                }
                                if (abs(numerator) >= denominator){
                                        s += Long.toString(abs(numerator) / denominator) + " ";
                                }
                                if (abs(numerator) % denominator != 0){
                                        s += Long.toString(abs(numerator) % denominator);
                                }else{
                                        s = s.substring(0, s.length()-1);
                                }
                                if (denominator != 1){
                                        s += "/" + Long.toString(denominator);
                                }
                                return s;
                        }
                       
                        public Fraction add(Fraction f){
                                Fraction fResult = new Fraction();
                                fResult.denominator = lcm(denominator, f.denominator);
                                fResult.numerator = numerator * fResult.denominator / denominator + f.numerator * fResult.denominator / f.denominator;
                                fResult.Cancellation();
                                return fResult;
                        }
                       
                        public Fraction subtract(Fraction f){
                                Fraction fResult = new Fraction();
                                fResult.denominator = lcm(denominator, f.denominator);
                                fResult.numerator = numerator * fResult.denominator / denominator - f.numerator * fResult.denominator / f.denominator;
                                fResult.Cancellation();
                                return fResult;
                        }
                       
                        public Fraction multiply(Fraction f){
                                Fraction fResult = new Fraction();
                                fResult.numerator = numerator * f.numerator;
                                fResult.denominator = denominator * f.denominator;
                                fResult.Cancellation();
                                return fResult;
                        }
                       
                        public Fraction divide(Fraction f){
                                Fraction fResult = new Fraction();
                                fResult.numerator = numerator * f.denominator;
                                fResult.denominator = denominator * f.numerator;
                                fResult.Cancellation();
                                return fResult;
                        }
                       
                        @Override
                        public int compareTo(Fraction f){
                                long g = gcd(denominator, f.denominator);
                                long res = numerator * (f.denominator / g) - f.numerator * (denominator / g);
                                if (res < 0){
                                        return -1;
                                }
                                if (res > 0){
                                        return 1;
                                }
                                return 0;
                        }
                       
                        public Fraction clone(){
                                Fraction fResult = new Fraction(numerator, denominator);
                                return fResult;
                        }
                       
                        public Fraction floor(){
                                Fraction fResult = this.clone();
                                fResult.numerator = (fResult.numerator / fResult.denominator) * fResult.denominator;
                                return fResult;
                        }
                       
                        public Fraction ceil(){
                                Fraction fResult = this.clone();
                                fResult.numerator = (fResult.numerator/fResult.denominator + 1) * fResult.denominator;
                                return fResult;
                        }
                       
                        public Fraction binpow(int n){
                                if (n==0) return FRACTION_ONE;
                                if ((n&1)==0){
                                        Fraction f=this.binpow(n/2);
                                        return f.multiply(f);
                                }else return binpow(n-1).multiply(this);
                        }
                }
               
                class FenwickTree_1{    //One-dimensional array        
                       
                        int n;
                        long[] t;
                       
                        public FenwickTree_1(int n){
                                this.n = n;
                                t = new long[n];
                        }
                       
                        public long sum(int xl, int xr){
                                return sum(xr) - sum(xl);
                        }
                       
                        public long sum(int x){
                                long result = 0;
                                for (int i = x; i >= 0; i = (i & (i + 1)) - 1){
                                        result += t[i];
                                }
                                return result;
                        }
                       
                        public void update(int x, long delta){
                                for (int i = x; i < n; i = (i | (i + 1))){
                                        t[i] += delta;
                                }
                        }
                }
               
                class FenwickTree_2{    //Two-dimensional array
                       
                        int n, m;
                        long[][] t;
                       
                        public FenwickTree_2(int n, int m){
                                this.n = n;
                                this.m = m;
                                t = new long[n][m];
                        }
                       
                        public long sum(int xl, int yl, int xr, int yr){
                                return sum(xr, yr) - sum(xl - 1, yr) - sum(xr, yl - 1) + sum(xl - 1, yl - 1);
                        }
                       
                        public long sum(int x, int y){
                                long result = 0;
                                for (int i = x; i >= 0; i = (i & (i + 1)) - 1){
                                        for (int j = y; j >= 0; j = (j & (j + 1)) - 1){
                                                result+=t[i][j];
                                        }
                                }
                                return result;
                        }
                       
                        public void update(int x, int y, long delta){
                                for (int i = x; i < n; i = (i | (i + 1))){
                                        for (int j = y; j < m; j = (j | (j + 1))){
                                                t[i][j] += delta;
                                        }
                                }
                        }
                }
               
                class FenwickTree_3{    //Three-dimensional array
                       
                        int n, m, l;
                        long[][][] t;
                       
                        public FenwickTree_3(int n, int m, int l){
                                this.n = n;
                                this.m = m;
                                this.l = l;
                                t = new long[n][m][l];
                        }
                       
                        public long sum(int xl, int yl, int zl, int xr, int yr, int zr){
                                return sum(xr, yr, zr) - sum(xl - 1, yr, zr)
                                + sum(xl - 1, yr, zl - 1) - sum(xr, yr, zl - 1)
                                - sum(xr, yl - 1, zr) + sum(xl - 1, yl - 1, zr)
                                - sum(xl - 1, yl - 1, zl - 1) + sum(xr, yl - 1, zl - 1);
                        }
                       
                        public long sum(int x, int y, int z){
                                long result = 0;
                                for (int i = x; i >= 0; i = (i & (i + 1)) - 1){
                                        for (int j = y; j >= 0; j = (j & (j + 1)) - 1){
                                                for (int k = z; k >= 0; k = (k & (k + 1)) - 1){
                                                        result += t[i][j][k];
                                                }
                                        }
                                }
                                return result;
                        }
                       
                        public void update(int x, int y, int z, long delta){
                                for (int i = x; i < n; i = (i | (i + 1))){
                                        for (int j = y; j < n; j = (j | (j + 1))){
                                                for (int k = z; k < n; k = (k | (k + 1))){
                                                        t[i][j][k] += delta;
                                                }
                                        }
                                }
                        }
                }
        }
}